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Homework Help: Proving that this set is a Dedekind cut.

  1. Apr 17, 2012 #1
    1. The problem statement, all variables and given/known data

    Cut.png

    2. Relevant equations

    In the above proplem, A is a dedekind cut.

    To be a cut:
    1. [itex]A \not= \mathbf{Q}[/itex] and [itex]A \not = \emptyset[/itex]
    2. If [itex]r \in A[/itex], then all [itex]s \in A[/itex] for all [itex]s \in \mathbf{Q}[/itex] such that [itex]s < r[/itex]
    3. A has no maximum


    I know the 3 properties by heart, but the set -A is so unwieldy, that I'm having difficulty proving each of these properties.
     
  2. jcsd
  3. Apr 17, 2012 #2

    Hurkyl

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    Staff Emeritus
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    Gold Member

    Then try things step-by-step. First, carefully write out what it is to be proven, incorporating the definition of -A....
     
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